A line passes through $(4, 9)$ $(4 ,9 )$ and $(5, 6)$ $(5 ,6 )$ . A second line passes through $(1, 8)$ $(1 ,8 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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A line passes through $(4, 9)$ $(4 ,9 )$ and $(5, 6)$ $(5 ,6 )$ . A second line passes through $(1, 8)$ $(1 ,8 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2017-10-30T09:01:27

$(2, 5)$ $(2,5)$

Explanation:

$one way is to establish the equation of the line passing$ $"one way is to establish the equation of the line passing"$
$through (1, 8) and evaluate for particular values of x$ $"through "(1,8)" and evaluate for particular values of x"$

$∙ parallel lines have equal slopes$ $• " parallel lines have equal slopes"$

$to calculate the slope (m) use the gradient formula$ $"to calculate the slope (m) use the "color(blue)"gradient formula"$

$color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x^2-x_1))color(white)(2/2)|)))$

$"let "(x_1,y_1)=(4,9)" and "(x_2,y_2)=(5,6)$

$rArrm=(6-9)/(5-4)=-3$

$rArry=-3x+blarrcolor(blue)"is the partial equation"$

$"to find b substitute "(1,8)" into the partial equation"$

$8=-3+brArrb=11$

$rArry=-3x+11larrcolor(red)"in slope-intercept form"$

$"choose any value for x and evaluate for y"$

$x=2toy=-6+11=5$

$rArr(2,5)" is a point on the second line"$

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A line passes through $(4, 9)$ $(4 ,9 )$ and $(5, 6)$ $(5 ,6 )$ . A second line passes through $(1, 8)$ $(1 ,8 )$ . What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

A line passes through (4 ,9 )(4,9)(4 ,9 ) and (5 ,6 )(5,6)(5 ,6 ). A second line passes through (1 ,8 )(1,8)(1 ,8 ). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer

Explanation:

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A line passes through $(4, 9)$ $(4 ,9 )$ and $(5, 6)$ $(5 ,6 )$ . A second line passes through $(1, 8)$ $(1 ,8 )$ . What is one other point that the second line may pass through if it is parallel to the first line?